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The following table gives the map coordinates and the shipping loads for a set of cities that we wish to connect through a central hub. City Map Coordinates (x,y) (4,10) (6,7) (5,8) (7,4) (8,8) (3,1) (2,7) a) For the location of the proposed new central hub, the coordinates should be near: x = 5.35 (round your response to two decimal places). y = (round your response to two decimal places). ;

The following table gives the map coordinates and the shipping loads for a set of cities that we wish to connect through a central hub. City Map Coordinates (x,y) (4,10) (6,7) (5,8) (7,4) (8,8) (3,1) (2,7) a) For the location of the proposed new central hub, the coordinates should be near: x = 5.35 (round your response to two decimal places). y = (round your response to two decimal places). ;

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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The following table provides the map coordinates and the shipping loads for a set of cities that are intended to be connected through a central hub. | City | Map Coordinates (x, y) | Shipping Load | |------|------------------------|---------------| | A | (4, 10) | 6 | | B | (6, 7) | 9 | | C | (5, 8) | 16 | | D | (7, 4) | 5 | | E | (8, 8) | 15 | | F | (3, 1) | 10 | | G | (2, 7) | 5 | a) For the location of the proposed new central hub, the coordinates should be near: - x = 5.35 (round your response to two decimal places). - y = [ ] (round your response to two decimal places).
Transcribed Image Text:The following table provides the map coordinates and the shipping loads for a set of cities that are intended to be connected through a central hub. | City | Map Coordinates (x, y) | Shipping Load | |------|------------------------|---------------| | A | (4, 10) | 6 | | B | (6, 7) | 9 | | C | (5, 8) | 16 | | D | (7, 4) | 5 | | E | (8, 8) | 15 | | F | (3, 1) | 10 | | G | (2, 7) | 5 | a) For the location of the proposed new central hub, the coordinates should be near: - x = 5.35 (round your response to two decimal places). - y = [ ] (round your response to two decimal places).
Expert Solution
WORKING NOTES

When establishing a single facility, the center of gravity approach takes into account the locations of existing facilities, the distances between them, and the amount of cargo that has to be transported.

We know that formula:

X-Coordinate = Sum of (X * Shipping load) / Total shipping load.

Y-Coordinate = Sum of (Y * Shipping load) / Total shipping load.

Now, Total shipping load = 6 +9 + 16 + 5 + 15 + 10 + 5 = 66

 

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